This invention relates generally to magnetic resonance imaging; and more particularly the invention relates to a method of mapping the B.sub.1 radio frequency field used in nuclei spin excitation.
Inhomogeneity of the radio-frequency (RF) field B.sub.1 interferes with many imaging methods, particularly those sensitive to flip angle such as fat saturation. Adiabatic excitation pulses are often used to overcome the effects of B.sub.1 inhomogeneity, at the cost of increased excitation time and considerably increased pulse power.
With a map of the B.sub.1 field over an imaging plane, multi-dimensional pulses could be designed to compensate for B.sub.1 inhomogeneity without the increased power requirements of adiabatic pulses. Since the B.sub.1 field achieved by a coil during excitation is also the sensitivity of the coil during reception, a map of the B.sub.1 field serves also as a map of coil sensitivity, which can be used for image intensity correction for scans utilizing a surface coil. Efforts have been made to correct image intensity with a theoretical B.sub.1 map calculated from coil geometry. In practice, factors such as coil imperfections and body geometry with locally varying complex dielectric constants may cause the actual B.sub.1 field to vary from its calculated ideal configuration.
Several methods of B.sub.1 mapping have been suggested. The simplest involves filling the entire imaging volume with a uniform water-filled sample, performing a simple imaging sequence, and interpreting the magnitude of the resulting image as a map of sin .alpha., where .alpha. is the flip angle and thus a measure of the B.sub.1 field. This method is subject to error from any factor other than B.sub.1 homogeneity that causes variation in the magnitude of the received image. This method also has very poor SNR characteristics for flip angles around 90.degree., since the derivative d.vertline.M.sub.xy.vertline./d.alpha. of the magnitude M.vertline.xy.vertline. of transverse magnetization with respect to flip angle .alpha. is zero for .alpha.=90.degree.. The derivative d.vertline.M.sub.xy.vertline./d.alpha. is maximum at .alpha.=0, but at this point the signal is zero.
Similarly, an imaging experiment may be repeated many times, changing the transmit gain of the RF amplifier with each repetition. The image in which a given voxel achieves its maximum magnitude corresponds to the transmit gain which most nearly produced a 90.degree. flip angle in that voxel. This method removes the effects of factors other than B.sub.1 inhomogeneity affecting image magnitude, but has the same SNR disadvantage as the previous method and requires many scans to achieve reasonable accuracy.
A similar method prepends a large-flip-angle pulse (nominally .alpha.=360.degree.) to a fast gradient-recalled echo (GRE) imaging sequence, varying the intensity of the pulse with successive scans. The magnitude of the image obtained is a function of the longitudinal magnetization M.sub.z remaining after the .alpha. pulse, and is maximum when .alpha.=360.degree.. However, since M.sub.z .alpha. cos .alpha., the derivative d.vertline.M.sub.xy.vertline./d.alpha. of the magnitude M.vertline..sub.xy.vertline. of the traverse magnetization with respect to the flip angle .alpha. of the prepended pulse is zero for .alpha.=360.degree., so this method suffers from the same SNR disadvantage as the previous two methods.
Oh et al Radio frequency field intensity mapping using a composite spin-echo sequence, Magn. Reson. Imaging 8, 21-25 (1990) proposed a phase-sensitive method of B.sub.1 mapping that uses a slice-selective 90.degree. excitation followed by a non-selective 90.degree..sub.x -180.degree..sub.y -90.degree..sub.x composite pulse. They showed that if only the 180.degree. part of the composite pulse is subject to B.sub.1 inhomogeneity, the resulting transverse magnetization has a phase which is a function of the actual flip angle achieved by the 180.degree..sub.y portion of the composite pulses. Their analysis assumed that the three 90.degree. pulses in the sequence were unaffected by B.sub.1 inhomogeneity. They also addressed main field (B.sub.0) inhomogeneity but assumed that this inhomogeneity was in effect only for the duration of the composite pulse, and neglected phase accrual due to inhomogeneity between the initial slice-selective 90.degree. pulse and the composite pulse. Unfortunately, when such phase accrual is factored in and all RF pulses in the sequence are made subject to the same B.sub.1 inhomogeneity, the phase of the resulting signal is no longer a single-valued function of B.sub.1 . In addition, since the composite pulse is not slice-selective, and since the 90.degree..sub.x elements of this pulse are subject to B.sub.1 inhomogeneity just as the 180.degree..sub.y element is, the out-of-slice signal generated by the composite pulse is potentially many times greater than the desired in-slice signal.
Insko et al. Mapping of the radiofrequency field, J. Magn. Reson. 103. 82-85 (June 1993) have described a method employing the ratio of acquisitions following .alpha.-.tau.-2.alpha. and 2.alpha.-.tau.-4.alpha. spin-echo excitations. The resulting ratio is a function of the actual flip angles achieved. This method has the advantage of being insensitive to main field B.sub.0 inhomogeneity. However, it is suitable for use over only a small range of tip angles, over which it has good sensitivity. Insko also proposed a variation of this technique in which the ratio of two gradient-echo acquisitions is obtained, with the idea that this method may be more suitable for a wider range of flip angles.
Topp et al. Fast multislice b.sub.1 -mapping, in "Proc., ISMRM, 5th Annual Meeting, Vancouver, April 1997," p.281, has recently suggested a method of B.sub.1 mapping with stimulated echoes formed by a slice-selective 90.degree. pulse which is followed by a large dephasing gradient lobe. A subsequent 90.degree. pulse encodes the resulting dephased transverse magnetization in the z axis. A non-selective pulse is then applied which has a nominal tip angle of .theta., followed by another 90.degree. tip and rephasing lobe which create a stimulated echo from the dephased magnetization stored in z. The magnitude of the signal obtained is proportional to cos .theta.. This sequence is repeated four times, with nominal values of .theta.=0.degree., 100.degree., 200.degree., and 300.degree.. A best fit of cos .theta. to the magnitude of the four actual acquisitions is calculated by a least-squares non-linear curve fitting algorithm.
We propose a phase-sensitive method of B.sub.1 mapping which has good signal-to-noise (SNR) properties over a wide range of B.sub.1 inhomogeneity corresponding to flip angles between 35.degree. and 145.degree.. This method may be suitable for mapping the wide variability of RF field strength and coil sensitivity encountered when surface coils are used for excitation and/or readout.